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As shown in the figure above, there is an in-extensive massless flexible thread. It is not tight at first so tension is $0$.

If I leave the object to free-fall, it reaches the bottom. Tension, which appears suddenly when the object reaches bottom, makes the object stop. At this moment should the tension be infinity? Or if it has an finite value, how can I calculate? (Eventually the tension would be $mg$ but to make the object stop I think it should be bigger when the object first reaches the bottom)

Qmechanic
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scitamehtam
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  • When you say "in-extensive" do you mean it doesn't stretch at all? In that case the tension could go to infinity. For any real world thread, it would be limited by the elastic modulus of the thread and Hooke's law. – The Photon Jan 20 '20 at 05:37
  • @ThePhoton why do you not write this as a two sentence answer? I learned the hard way that comments can disappear, and the questioner remains without the answer given in a comment. – anna v Jan 20 '20 at 05:43
  • @annav, because I don't know what "in-extensive" means. – The Photon Jan 20 '20 at 05:45

2 Answers2

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If the thread is inextensible and massless, the body will immediately come to a stop the moment the thread becomes taut. Since this happens instantaneously, the force experienced by the string will be infinite for that small moment.

However, realistically no string satisfies the above conditions. The threads will have some elasticity as well as a limiting tension value.

Sam
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To answer to a real world problem assumptions have to made.
In this case an assumption is made, the thread is massless and inextensible, which leads to a solution, for an instant of time the thread exerts an infinite force on the mass, the mass undergoes an infinite acceleration, the speed of the mass becomes zero instantaneously, which is not the experience of the real world.
One then has to go back to see which assumptions about the system have lead to this result.
In this case it is the fact that the thread is inextensible.
In the real world the thread would stretch and like a spring exerted a finite force on the mass which would reduce its speed to zero over a finite amount of time.
Depending on the amount of friction present there may also be an oscillatory phase as one would observe when a mass is released at the end of an unextended spring,

Related answer - Can an object immediately start moving at a high velocity?

Real world example of the "threads" designed to make the retarding force smaller are bungee ropes and climbing ropes which stretch quite a lot when under tension.

Farcher
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